Elementary statistics

Question

Suppose a 6-sided die is weighted so that the probability of an outcome is proportional to the outcome. That is, P p P p P p P p P p P p (1 2 2 3 3 4 4 5 5 6 6 ) = = = = = = ( ) ( ) ( ) ( ) ( ) (here p stands for a mystery number) a) (2.5pts) Find the value of p that would make this a valid probability model and then state the exact (in fraction form) probability of rolling each number on the die. b) (1.5pts) Which of the following events is more likely: rolling a 6 or rolling a or 1 2 ? Use your work from part (a) to justify your answer.

Answer 1

The first thing to realize is that the probability of a number being proportional means P(6) is 6 time more likely than P(1) and so on. Therefore takin P(1) as p, the sum of the probabilities = 1 = (1+2+3+4+5+6)p = 21p. So, the probabilities of the numbers appearing are 1/21, 2/21,...6/21)

In b, just compare p(6) to p(1)+p(2)